Rubber entanglement constraints

Two monomer units cannot occupy the same space, and two chains cannot pass through each other. These entanglement constraints are not easy to introduce into the theory of rubber elasticity though many attempts have been made. 

Some of the most interesting advances in the theory of rubber elasticity are the various approaches being developed to take better account of chain entanglements [22, 30]. In the constraint theories, the focus is on the way the constraints are placed within the network structure, as discussed in the following section. 

More recent network models of rubber elasticity by Ronca and Allegra [11] and Hory and Erman [12] are based on the phantom network model but assume that the junction point fluctuations are restricted due to the presence of entanglements. The strength of the constraints is defined by a parameter... 

Recent experimental advances reinforce the idea that the microscopic motions and the elastic properties can be usefully interrelated. For example, quasielastic neutron scattering measurements probe the motions of the network junctions [53,54]. Molecular dynamics simulations have also added new insight, for example, by demonstrating the existence of local constraints on the network chains at strand lengths less than the molecular weight necessary for chain entanglements [55]. Recently P NMR spin-lattice relaxation experiments on crosslinked rubber have been used to monitor specifically the dynamics of the network junctions [52,56]. 

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